Theorems · Theorem · linear algebra

Submodule.span_coe_eq_restrictScalars

∀ {R : Type u_1} {M : Type u_4} {S : Type u_7} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (p : Submodule R M) [inst_3 : Semiring S] [inst_4 : SMul S R] [inst_5 : Module S M] [inst_6 : IsScalarTower S R M],
  Submodule.span S ↑p = Submodule.restrictScalars S p

A version of Submodule.span_eq for when the span is by a smaller ring.

Defined in

Mathlib.LinearAlgebra.Span.Basic

Cited by

13 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidModuleSemiringSMulModuleIsScalarTower